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Symmetry and Integrability of Classical Field Equations

Authors
  • Papachristou, C. J.
Type
Published Article
Publication Date
May 14, 2008
Submission Date
Mar 26, 2008
Identifiers
arXiv ID: 0803.3688
Source
arXiv
License
Yellow
External links

Abstract

A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to the symmetry problem of PDE's is described, suitable for PDE's the solutions of which are non-scalar fields (e.g., are in the form of matrices). A method is proposed which, in certain cases, may "unify" the symmetry and integrability properties of a nonlinear PDE. Application is made to the self-dual Yang-Mills equation and the Ernst equation of General Relativity.

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